Properties

Level $68$
Weight $0$
Character 68.1
Symmetry even
Fricke sign $-1$

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Maass form invariants

Level: \( 68 = 2^{2} \cdot 17 \)
Weight: \( 0 \)
Character: 68.1
Symmetry: even
Fricke sign: $-1$
Spectral parameter: \( 2.30438766562 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.000000000\) \(a_{3}=-0.554934027\) \(a_{4}=+0.000000000\) \(a_{5}=-1.005148870\)
\(a_{6}=+0.000000000\) \(a_{7}=+1.302694496\) \(a_{8}=+0.000000000\) \(a_{9}=-0.692048225\) \(a_{10}=+0.000000000\)
\(a_{11}=-1.620689608\) \(a_{12}=+0.000000000\) \(a_{13}=+1.252141810\) \(a_{14}=+0.000000000\) \(a_{15}=+0.557791310\)
\(a_{16}=+0.000000000\) \(a_{17}=-0.242535625\) \(a_{18}=+0.000000000\) \(a_{19}=-1.770733236\) \(a_{20}=+0.000000000\)
\(a_{21}=-0.722909503\) \(a_{22}=+0.000000000\) \(a_{23}=-0.648655988\) \(a_{24}=+0.000000000\) \(a_{25}=+0.010324250\)
\(a_{26}=+0.000000000\) \(a_{27}=+0.938975136\) \(a_{28}=+0.000000000\) \(a_{29}=-0.273152340\) \(a_{30}=+0.000000000\)
\(a_{31}=+0.114958140\) \(a_{32}=+0.000000000\) \(a_{33}=+0.899375811\) \(a_{34}=+0.000000000\) \(a_{35}=-1.309401900\)
\(a_{36}=+0.000000000\) \(a_{37}=+1.024964516\) \(a_{38}=+0.000000000\) \(a_{39}=-0.694856097\) \(a_{40}=+0.000000000\)
\(a_{41}=+0.761755836\) \(a_{42}=+0.000000000\) \(a_{43}=-0.912316663\) \(a_{44}=+0.000000000\) \(a_{45}=+0.695611492\)
\(a_{46}=+0.000000000\) \(a_{47}=+0.908014606\) \(a_{48}=+0.000000000\) \(a_{49}=+0.697012949\) \(a_{50}=+0.000000000\)
\(a_{51}=+0.134591271\) \(a_{52}=+0.000000000\) \(a_{53}=-0.184551475\) \(a_{54}=+0.000000000\) \(a_{55}=+1.629034328\)
\(a_{56}=+0.000000000\) \(a_{57}=+0.982640126\) \(a_{58}=+0.000000000\) \(a_{59}=-1.682287067\) \(a_{60}=+0.000000000\)
\(a_{61}=-1.057122963\) \(a_{62}=+0.000000000\) \(a_{63}=-0.901527414\) \(a_{64}=+0.000000000\) \(a_{65}=-1.258588925\)
\(a_{66}=+0.000000000\) \(a_{67}=-0.811440443\) \(a_{68}=+0.000000000\) \(a_{69}=+0.359961280\) \(a_{70}=+0.000000000\)
\(a_{71}=-0.299895398\) \(a_{72}=+0.000000000\) \(a_{73}=+1.347065243\) \(a_{74}=+0.000000000\) \(a_{75}=-0.005729278\)
\(a_{76}=+0.000000000\) \(a_{77}=-2.111263432\) \(a_{78}=+0.000000000\) \(a_{79}=+0.902979629\) \(a_{80}=+0.000000000\)
\(a_{81}=+0.170978972\) \(a_{82}=+0.000000000\) \(a_{83}=-0.988571063\) \(a_{84}=+0.000000000\) \(a_{85}=+0.243784409\)
\(a_{86}=+0.000000000\) \(a_{87}=+0.151581528\) \(a_{88}=+0.000000000\) \(a_{89}=-1.234332215\) \(a_{90}=+0.000000000\)
\(a_{91}=+1.631158243\) \(a_{92}=+0.000000000\) \(a_{93}=-0.063794184\) \(a_{94}=+0.000000000\) \(a_{95}=+1.779850511\)
\(a_{96}=+0.000000000\) \(a_{97}=-0.256813492\) \(a_{98}=+0.000000000\) \(a_{99}=+1.121595368\) \(a_{100}=+0.000000000\)

Showing 100 of 598 available coefficients

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